Joseph D. Fehribach

Mechanistic and Bifurcation Analysis of Anode Potential Oscillations in PEMFCs with CO in Anode Feed

A detailed mathematical analysis is performed to understand the anode potential oscillations observed experimentally in a proton exchange membrane fuel cell (PEMFC) with H 2 /CO feed (Ref. 9). Temperature and anode flow rate are found to be key bifurcation parameters. The time dependence of all the key surface species must be accounted for in order for the model to predict the oscillatory behavior, while the time dependence of CO concentration in the anode chamber need not necessarily be considered. The bifurcation diagram of CO electro-oxidation rate constant agrees very well with the effect of temperature on the oscillation pattern. The oscillator model is classified as a hidden negative differential resistance oscillator based on the dynamical response of the anodic current and surface species to a dynamic potential scan. A linear stability analysis indicates that the bifurcation experienced is a supercritical Hopf bifurcation.

A Three‐Phase Homogeneous Model for Porous Electrodes in Molten‐Carbonate Fuel Cells

In this paper a new model for porous electrodes in molten-carbonate fuel cells (MCFC) is presented. The model is based on an averaging technique commonly used in porous-media problems. Important disadvantages of the existing agglomerate model caused by geometric assumptions and restrictions are eliminated in this new model. Unlike the agglomerate model, the new model is suitable for studying three-dimensional and anisotropic problems and incorporating the degree of electrolyte fill. Different reaction mechanisms can easily be incorporated. The validity of the new model is checked and compared with the agglomerate model by fitting the two models to ac-impedance spectra recorded from porous MCFC cathodes.

On modelling molten carbonate fuel-cell cathodes by electrochemical potentials

We derive an electrochemical-potential model for the peroxide mechanism describing the electrochemistry of a molten carbonate fuel cell cathode. The advantages of this model include elegantly combining the chemical and electrical processes, making clear the connection to the underlying reaction stoichiometry, and requiring the fewest equations consistent with that stoichiometry. The relationship between electrochemical-potential and concentration models is also discussed, along with a two-dimensional computational study of the effects of variations in electrode geometry or coefficient parameters. In particular, it is shown that the mean current density associated with a small portion of electrode may be increased by as much as a factor of five by carefully redistributing the electrolyte, and that on this scale the current density is most sensitive to the electrolyte diffusivity.

Triple Phase Boundaries in Solid-Oxide Cathodes

Component potential modeling based on solid-oxide electrochemistry is used to study a single-particle configuration where a hemispherical LSM particle sits on a YSZ electrolyte half-space. The primary comparison is between two pathways: one where oxide ions travel on the particle surface; the other where these ions travel through the bulk particle interior. The systems that model each of the pathways are analyzed both mathematically and numerically, yielding insights into diffusion-reaction-conduction processes for this single-particle model. A broad range of parameter values are considered, particularly in regards to the least well-established value, the surface conductance for the surface pathway. This work includes a number of case studies that indicate which pathway dominates for a variety of parameter choices.

Diffusion-Reaction-Conduction Processes in Porous Electrodes: The Electrolyte Wedge Problem

This work studies mathematical issues associated with steady-state modelling of diffusion-reaction-conduction processes in an electrolyte wedge (meniscus corner) of a current-producing porous electrode. The discussion is applicable to various electrodes where the rate-determining reaction occurs at the electrolyte-solid interface; molten carbonate fuel cell cathodes are used as a specific example. New modelling in terms of component potentials (linear combinations of electrochemical potentials) is shown to be consistent with tradition concentration modelling. The current density is proved to be finite, and asymptotic expressions for both current density and total current are derived for sufficiently small contact angles. Finally, numerical and asymptotic examples are presented to illustrate the strengths and weaknesses of these expressions.

NEW EXACT SOLUTIONS FOR A FREE BOUNDARY SYSTEM

A method for constructing explicit exact solutions to nonlinear evolution equations is further developed. The method is based on consideration of a fixed nonlinear partial differential equation together with an additional generating condition in the form of a linear high-order ordinary differential equation. The method is then applied to a free boundary problem based on the process of precipitant-assisted protein crystal growth.

Estimates for Polarization Losses in Molten Carbonate Fuel Cell Cathodes

This paper compares the polarization losses associated with the various diffusion-reaction-conduction processes in molten carbonate cathodes. The comparisons are made by estimating each type of loss in terms of component electrochemical potentials in joules/mole; this allows diffusive, charge-transfer, and ohmic losses to all be put on equal footing. For characteristic parameter values, diffusion in both the gas and electrolyte phases and conduction in the electrolyte account for similar polarization losses: charge-transfer and conduction in the solid electrode account for significantly smaller losses. These results tend to support and unify the previous work of numerous investigators. Also molecular-channel interactions are found not to contribute significantly to the polarization loss.

Matrices and their Kirchhoff graphs

The fundamental relationship between matrices over the rational numbers and a newly defined type of graph, a Kirchhoff graph, is established. For a given matrix, a Kirchhoff graph represents the orthogonal complementarity of the null and row spaces of that matrix. A number of basic results are proven, and then a relatively complicated Kirchhoff graph is constructed for a matrix that is the transpose of the stoichiometric matrix for a reaction network for the production of sodium hydroxide from salt. A Kirchhoff graph for a reaction network is a circuit diagram for that reaction network. Finally it is conjectured that there is at least one Kirchhoff graph for any matrix with rational elements, and a process for constructing an incidence matrix for a Kirchhoff graph from a given matrix is discussed.

Vector-Space Methods and Kirchhoff Graphs for Reaction Networks

This article presents a vector-space formulation for constructing reaction routes (reaction pathways) and Kirchhoff graphs (reaction route graphs, fundamental graphs) for reaction networks. Specific examples from fuel-cell electrochemistry are included throughout to illustrate the more general theoretical discussion. Some of the mathematical aspects of Kirchhoff graphs, such as their representation of the fundamental theorem of linear algebra, are also discussed.

The Use of Graphs in the Study of Electrochemical Reaction Networks

The purpose of this chapter is to review and discuss the uses of graphs in the study of chemical and particularly electrochemical reaction networks. Such reaction networks are defined by (often elementary) reaction steps, and in turn the total chemical process associated with a given set of reaction steps is its reaction network. Such a network should normally determine at least one overall reaction. Certain steps in a given reaction network may occur at specified locations, and the overall process may involve transport between these locations. Graphs have long been used in various ways to clarify all of these concepts. In what follows, any graph used to study a reaction network will be termed a reaction graph. Although there have been many such uses over the years, there are three general categories which largely cover all uses of graphs: